mechanics

• ​kinematics

  • ​equations of motion

    • ​条件：constant acceleration in a straight line

    • ​ $v =u+at$ 

    • ​ $s=\frac{u+v}{2} t$ 

    • ​ $s=ut+\frac{1}{2}at^{2}$ 

    • ​ $v^{2} =u^{2}+2as$ 

    • ​ $s=vt-\frac{1}{2}at^{2}$ 

    • ​note: positive direction 

  • ​graphs

    • ​v-t graph

    • ​s-t graph

    • ​a-t graph

  • ​projectiles

    • 平抛

      • ​horizontal：constant velocity

      • ​vertical：free fall

    • ​斜抛

      • ​horizontal: constant veloctiy

      • ​vertical: constant acceleration

• ​dynamics

  • ​Newton's laws of motion

    • ​first law

    • ​second law

      • ​F=ma

        • ​F-resultant force
          

      •  $F=\frac{ \triangle p}{ \triangle t}$ 

        
        

    • ​third law

  • ​all kinds of forces

    • ​weight

    • ​normal force

    • ​friction

    • ​viscous force/drag/air resistance

  • ​top speed

  • ​motion on an inclined plane

• ​moments

  • ​moment of a force--definition

  • ​equilibrium condition--principle of moment

  • ​torque of  a couple

• ​work, energy, power

  • ​work done=force×distance moved in the direction of the force

  • $$$k.e.=\frac{ 1}{ 2}m v^{2}$ rac{ 1}{ 2}

  • ​ $g.p.e.=mgh$ 

  • ​principle of conservation of energy

  • ​work done = energy transferred

  • ​ $P=\frac{W}{t}$   /  $P=Fv$ 

• ​momentum

  • ​ $p=mv$ 

  • ​collision

    • ​(perfectly) elastic collision

      • ​1. conservation of momentum

      • ​2. conservation of k.e.

      • ​3. relative speed unchanged

    • ​inelastic collision

      • ​1. conservation of momentum

      • ​2. k.e. before collision > k.e. after collision

    • ​collisions in two dimensions

  • ​​Newton's laws of motion and momentum

• ​deformation

  • ​elastic deformation

    • ​Hooke's law  $F=kx$ 

    • ​force-extension graph

      • ​gradient=k

      • ​area under graph=elastic potential energy/work done

    • ​proportional limit & elastic limit

    •  $stress=\frac{force}{cross-sectional area}$    $σ =\frac{F}{A}$ 

    • ​ $strain =\frac{ extension}{original length}$ 

    • ​stress-strain graph

      • ​gradient=E

    • ​Young modulus= $\frac{ stress}{strain}$     $E=\frac{ σ }{ ε }$ 

      • ​ $k=\frac{ EA }{ L }$ 

    • ​elastic potential energy / strain energy

      • ​ $E=\frac{ 1}{ 2 }Fx$ 

      • ​ $E=\frac{ 1}{ 2 } x^{2}$ $E=\frac{ 1}{ 2 }k x^{2}$ 

  • ​plastic deformation